A common situation in practical industrial applications related to product development is the need to perform quick surveys inside a space of state parameters. In mature and very competitive industrial sectors like aerospace, this need is motivated by the drive to generate products having good technical performance within design cycles that are as short as feasible. That is: time is a key factor in aerospace competitiveness because shortening the time market may provide a leading economic advantage during the product life cycle.
In the specific case of aeronautics, the prediction of the aerodynamic forces, and more generally skin surface values distributions, experienced by an aircraft is an important feature, in order to optimally design its structural components so that the weight of the structure is the minimum possible, but at the same time being able to withstand the expected aerodynamic forces.
Thanks to the increase of the use of the Computer Fluid Simulation Capability, nowadays, the determination of the aerodynamic forces on an aircraft is commonly done by solving numerically the Reynolds Averaged Navier-Stokes equations (RANS equations from now onwards) that model the movement of the flow around the aircraft, using discrete finite elements or finite volume models. With the demand of accuracy posed in the aeronautical industry, each one of these computations requires important computational resources.
The dimensioning aerodynamic forces are not known a priori, and since the global magnitude of the forces may depend on many different flight parameters, like angle of attack, angle of sideslip, Mach number, control surface deflection angle, it has been necessary to perform many lengthy and costly computations to properly predict the maximum aerodynamic forces experienced by the different aircraft components or the complete aircraft.
In order to reduce the overall number of these lengthy computations, approximate mathematical modelling techniques have been developed in the past, like Single Value Decomposition (SVD) as a means to perform intelligent interpolation, or the more accurate Proper Orthogonal Decomposition (POD from now onwards) that takes into account the physics of the problem by using a Galerkin projection of the Navier-Stokes equations.
The idea of these techniques is to define the new analytical solution as a combination of the information obtained before. POD defines several modes that include the solution obtained by Computational Fluid Dynamics (CFD) and then uses those modes to reproduce solutions not obtained by CFD. The more modes used the best with the limitation that the maximum number of modes is the number of snapshots.
But it is known in the art that these POD methods based in Galerkin equations, attractive as they are, need stabilisation schemes to yield acceptable solutions, but still with the risk that an erroneous state of the POD-reduced order model equations may be obtained after a long-time even if the correct state is set to initialise the simulation. This stability problem of the POD Galerkin projection based methods has prevented their usage from an industrial point of view.
The present invention is intended to solve this drawback.